Math teacher 🇲🇦 · AI Researcher · Builder of Humble Systems
"The universe is learning by doing, not by learning about doing."
I'm a mathematician and AI researcher from Morocco exploring mathematical foundations for intelligence, optimization, and information processing systems.
My current focus is a long-term research project emerging from my work on Humble Systems Theory and reinforcement learning.
A Humble Philosophical Attempt to Build the Mathematical Foundation for Complex-Valued Reinforcement Learning
This repository is currently my main research focus. It is an attempt to develop, step by step, a mathematical foundation for complex-valued reinforcement learning, connecting ideas from reinforcement learning, mathematical analysis, geometry, stochastic processes, optimization, and my broader work on Information Processing Systems.
At the moment, the repository contains only two chapters. However, based on the papers I have been studying, the mathematical directions emerging from the work, and many ongoing discussions with AI, I currently estimate that the complete project may eventually contain roughly 19 chapters.
That number is only an estimate. The structure will probably change substantially as the research develops.
The repository is still messy, incomplete, and actively changing.
I don't expect to finish it quickly. My current estimate is that it may take somewhere between 6 months and a year before I feel that the work is sufficiently developed and organized.
There is a lot to do: research reviews, mathematical development, writing, experiments, and code. Some ideas will probably be discarded, others rewritten, and some may lead somewhere I don't currently expect.
So this repository should be considered a living research notebook evolving toward a larger mathematical work, rather than a finished theory.
One of the biggest difficulties so far is that I am still the only contributor to the theory itself.
I have been developing these ideas largely on my own, and I haven't yet managed to start the kind of serious discussion around them that would allow other researchers to challenge the assumptions, find mistakes, suggest alternatives, or help develop the mathematics.
If you are interested in the foundations of reinforcement learning, complex-valued mathematics, mathematical modeling, information processing systems, or related areas, discussion, criticism, corrections, and collaboration are very welcome.
My broader research direction is Humble Systems Theory (HST) — a framework exploring Information Processing Systems (IPS) as systems that receive information, pay computational costs, pursue goals, operate under constraints, and affect future states.
One of the mathematical objects emerging from this work is the complex-valued quantity
Q(sᵢ, sⱼ) = cost(sᵢ, sⱼ) + i · debt(sᵢ, sⱼ)
The complex structure is intended to represent more than simply adding another numerical dimension. It is part of an attempt to investigate whether reinforcement learning can be formulated using a richer mathematical representation of cost, debt, state transitions, and system dynamics.
Artificial Intelligence · Mathematical Modeling · Information Geometry · Reinforcement Learning · Python · PyTorch · Physics · Optimization
I'm not trying to pretend that the theory is finished. I'm trying to build it carefully enough that other people can eventually break it, criticize it, improve it, or prove parts of it wrong.
The repository is the experiment.
Open to collaboration, criticism, mathematical discussion, and anyone interested in helping develop the ideas.
δ > 0, always and necessarily.